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Abstract

Ring exchange is an elementary interaction for modelling unconventional topological matter. Here, we report the observation of four-body ring-exchange interactions and the topological properties of anyonic excitations within an ultracold atom system. A minimum toric-code Hamiltonian, in which the ring exchange is the dominant term, was implemented in disconnected four-spin plaquette arrays formed by two orthogonal superlattices. The ring-exchange interactions were resolved from the dynamical evolutions of the spin orders in each plaquette, matching well with the predicted energy gaps between two anyonic excitations of the spin system. A braiding operation was applied to the spins in the plaquettes and an induced phase 1.00(3)π in the four-spin state was observed, confirming 1/2 mutual statistics. This work offers new prospects for the quantum simulation of topological phases by engineering many-body interactions.

Acknowledgements

We thank A. J. Leggett, P. Zoller and B. Zhao for helpful discussions. This work was supported by the National Key R&D Program of China (2016YFA0301600), National Natural Science Foundation of China (91421305, 11521063), and the Chinese Academy of Sciences.

Author information

Author notes

Han-Ning Dai

& Bing Yang

These authors contributed equally to this work.

Affiliations

Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

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Contributions

Y.-A.C., Z.-S.Y. and J.-W.P. initiated and designed this research project. H.-N.D., B.Y., A.R., X.-F.X. and Z.-S.Y. set up the experiment. H.-N.D., B.Y., A.R. and H.S. performed the measurement and analysed the data. All authors contributed to manuscript preparation. Z.-S.Y. and J.-W.P. supervised the whole project.